ThermoLIB -- A Python Library for Constructing and Post-Processing Free Energy Surfaces to Extract Thermodynamic and Kinetic Properties

TL;DR

ThermoLIB addresses the challenge of extracting reliable thermodynamic and kinetic information from enhanced-sampling simulations by providing a unified post-processing framework. It couples a maximum-likelihood WHAM formulation with Fisher-information-based error propagation to yield accurate free-energy surfaces $F(q)$ with full covariance. The package enables a posteriori transformations, projections, and deprojections between CVs and provides a CV-independent kinetic-rate analysis via transition-state theory, including consistent uncertainty estimates. Tutorials and case studies demonstrate how ThermoLIB detects undersampling, recovers hidden mechanistic information, and delivers robust thermodynamic and kinetic quantities for complex molecular systems.

Abstract

ThermoLIB is Python/Cython library designed to be used as a post-processing tool for constructing free energy surfaces from the output of molecular simulations, transforming them between different collective variables (CVs) and extracting thermodynamic and kinetic information. ThermoLIB is available for download on GitHUB and comes with extended documentation as well as many tutorials. The implementation is based on the theory of maximum likelihood estimators and includes error bars on and full covariance matrix between all points on the free energy surface using the Fisher information matrix. The free energy surfaces can be transformed a posteriori to other collective variables, projected towards lower dimensional CV-spaces and even deprojected towards higher dimensional CV-spaces if additional information from the simulation is provided in the form of a conditional probability. Finally, one can extract usefull thermodynamic and kinetic properties such as the reaction free energy and kinetic rate constant. Error bars on the free energy surfaces are propagated throughout al these operations. We briefly illustrate the capabilities of ThermoLIB by means of some tutorials and case studies.

Figures (11)

• Figure 1: Typical workflow of a molecular simulation consisting of 4 steps, where ThermoLIB is a tool designed to evaluate sampling from step 3 and construct the properties from step 4. Figure adapted from Ref.VanSpeybroeck2023
• Figure 2: Illustration how a seemingly well converged 1D FEP (solid line top pane) did not result from adequate sampling. Investigating the visited states in a 2D phase space with an additional important CV (bottom pane) reveals two disjoint regions. Due to missing sampling (indicated by dot-dashed region) we have no information on the relative stability between these two parts of phase space and do not know the free energy difference between these states. In other words, the true uncertainty on the computed FEP should actually diverge to infinite once the two regions start to overlap along $Q$.
• Figure 3: Illustration of a formic acid dimer and the coordination numbers used in the definition of the collective variable
• Figure 4: Trajectory analysis of the various umbrella simulations. (a) Mean of CV for each umbrella simualtion allowing to interpret which part of phase space each simulation covers (b) Overlap matrix between the histograms of each pair of umbrella simulations (c) Overlap of each umbrella simulation with its right neighbor (in red) or second right neighbor (in blue). The overlap threshold of $0.33$ is arbitrary, but represents (in general) a good rule of thumb.
• Figure 5: Autocorrelation time of the CV samples for each umbrella simulation.